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Estimating the Wizarding Population

So, I've noticed this subject has been touched on in quite a few threads, but I could not find any discussion specifically devoted to it. I welcome your input here (as well as anyone who'd like to challenge my assertions or question my math. ).

How big is the wizarding population?

This is quite significant if you are writing a story about wizarding culture, particularly in other countries, and you're making any attempt at "realistically" depicting what wizarding society would be like, coexisting with Muggles.

Evidence from the Books

Rowling, as she has admitted herself, is rubbish with numbers. She once gave a figure of ~1000 students at Hogwarts, but the evidence of the books (and the movies, which, while not canonical, have been given Rowling's seal of approval, which implies she doesn't think they're radically far off) suggests a figure closer to 200-300.

Other than that, we have little sense of just how many wizards there are from the books. Large enough to sustain Hogsmeade and Diagon Alley and all their associated businesses, but Hogsmeade is apparently the only all-wizarding community in Britain, and it's not very big. Large enough to have a Ministry with lots of Departments, not large enough to have a standing army. Large enough to have a big crowd at the Quidditch World Cup, but that was an international gathering, and certainly wasn't very large compared to the real World Cup.

Intuitively, I'd place the British wizarding population at somewhere below 50,000, but that number seems both too small for some purposes, and too large for others.

So, let's take a look at some ways we might estimate the population, and its implications. (Most facts cited below come from UN figures or the CIA World Factbook, and can easily be found on Wikipedia.)

In all cases, I will be using three population groups as examples: the UK, the USA, and the global population. Not meaning to slight any other countries, but for me, these three are the easiest and most relevant benchmarks.

Demographic Estimates from Birth Rates

If Hogwarts has ~1000 students, then we're looking at about 140 new students per year. If it's under 300, then only about 40 new students per year at most. That tells us something about the UK wizarding population's birth rate.

We have to make a few assumptions. First, assume that wizards have children at about the same rate as the surrounding Muggle population. (This is a convenient assumption, but may not be true! Wizards might breed like bunnies compared to Muggles – if the Weasleys are typical – or they might have fewer children on average.)

Second, we're basing birth rates on Hogwarts entry rates. We don't know what percentage of British wizarding children attend Hogwarts, but we're led to believe most do. I'll make a liberal estimate that up to half of British wizarding children don't attend Hogwarts, which is probably too large a figure, but it allows us a somewhat larger wizarding population. So that would imply a mere 280 births per year (at the high side), or 80 per year (on the low side).

Third, I am assuming that Squibs and Muggle-borns are rare enough to be statistically insignificant, and more or less cancel each other out.

Let's look at actual birth rates (as of 2007-2008):

World: 20.3/1000

UK: 10.65/1000

USA: 14/1000

(By way of comparison, the countries with the highest birth rates are up in the high 40s, while the countries with the lowest birth rates, including Germany and Japan, are down around 8/1000 or less.)

This may not be strictly accurate when comparing to the Hogwarts population given in the books, since they were set about 10 years ago, but I don't think birth rates have changed radically since then. I couldn't find a historical birth rates table.

Taking the UK figure of 10.65 per 1000, if British wizards reproduce at the same rate, then the high side estimate of 140 new births per year implies a British wizarding population of just a little over 13,000. The low side estimate (80 per year) gives us only about 7500 British wizards.

What does it mean in terms of the wizard population compared to the Muggle population?

By Comparison: Wizarding Population vs. Muggle Population

Here are the current total populations of our benchmarks:

World: 6.5 billion

UK: 61 million

USA: 305 million

Using the UK estimates, above, that would give a ratio of 1 wizard/4692 Muggles (on the high side) or 1 wizard/8133 Muggles (on the low side).

So, let's assume that any number of the above factors might be significantly off, and suggest a range of 1 wizard/2000 Muggles (which in the UK case, would require that wizards are all having Weasley-sized families in 2008, and/or that there were a lot of wizarding children we never saw who didn't go to Hogwarts) to 1 wizard/20,000 Muggles (an extremely conservative estimate, which assumes that I was too generous in each and every one of my assumptions). Below, I round figures a bit and assume that the ratio applies to the entire world, on average (in fact, there would likely be significant variations in the ratio from country to country).

Wizarding Population if the ratio is 1 wizard per 2000 Muggles(Maximum feasible ratio.)

World: 3.25 million

UK: 30.5K

USA: 152.5K

Wizarding Population if the ratio is 1 wizard per 4600 Muggles(Uses my high side estimate as more or less accurate.)

World: 1.41 million

UK: 13.26K

USA: 66.3K

Wizarding Population if the ratio is 1 wizard per 8100 Muggles(Uses my low side estimate as more or less accurate.)

World: 802,469

UK: 7,530

USA: 37,654

Wizarding Population if the ratio is 1 wizard per 20,00 Muggles(Minimum feasible estimate.)

World: 325,000

UK: 3050

USA: 15,250

Summary:

My rough calculations, with a range allowing for up to a 10-fold error in the net effects of all my assumptions, give us the following potential wizarding population ranges:

World: 325K – 3.25M

UK: 3050 – 30,500

USA: 15,250 – 152,500

Even at the upper end, this is a pretty small number. Is this is a large enough population to support the society we saw in the books? Is it large enough to support the idea of large wizarding corporations, railway networks, international confederations, and the like? If there are only about three thousand wizards in Britain, how are they all employed? Not everyone can work at the Ministry or in Hogsmeade or Diagon Alley. What does this imply about the scale of the war? Keep in mind that any way you look at it, these estimates are based on 2008, and so the numbers in the 70s and 90s would have been even smaller.

You can use these numbers to estimate how many wizards you might find in any given population group. (I, of course, am trying to project accurate figures for the American wizarding population in my Alexandra Quick series.) If you want to hypothesize entire towns full of wizards dotting a country, you need to think about how frequent and how populous those towns might be.

I am looking to refine my numbers and my methodology, so feedback is welcome.

It follows a similar line of reasoning to yours, and at least provides a sensible framework to base some numbers upon. As with a number of other ideas in her wizarding world, J.K. Rowling herself did not have a great strength in providing consistency of her own concepts.

It follows a similar line of reasoning to yours, and at least provides a sensible framework to base some numbers upon. As with a number of other ideas in her wizarding world, J.K. Rowling herself did not have a great strength in providing consistency of her own concepts.

Interesting -- I had not come across that essay before. Thanks!

I agree with the author that 600-1000 students really doesn't make much sense, which is why my own assumption has always been that Hogwarts' enrollment is more like 240-280 at any given time. She tries to make some guesses based on lifespan as well, and also factors half-bloods and Muggle-borns in (and seems to assume the latter are more common than I did).

I just realized that my figures above assume that almost all wizard births are purebloods -- I didn't factor in the likelihood that many would be half-bloods, one-quarter Muggle, etc. But the author you cited comes up with numbers that aren't too far from mine. (She tends towards the low side, and that's actually what I think is more likely as well.)

In my fic I had the UK as having ~3,000 (I don't remember where I got that from, I'll probably change it to 15,000 now that I look at at) and the US as having ~60,000.

I also put in a jab at the inconsistencies of the books.

"... Last I heard, the wizarding population of Britain was what, three thousand?”

"It depends on who you ask... There’s no centralized means of tracking who comes and goes. Some analysts try to estimate based on how many students are enrolled at Hogwarts at any one time, but even those numbers don’t make sense.”

In all reality, no one stopped loving the real books because of these discrepancies, so I doubt people will hound you if your numbers don't quite add up. Just pick a number you think works and go with it.